Finite Group Databasebeta

← #11895918

Subgroups — #11895918

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic, complemented
2#10596024C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4#10592862C212yesmaximal, complemented
5#10592726C211yesmaximal, characteristic, complemented
6#10592706C211yesmaximal, characteristic, complemented
7#10592570C212yesmaximal, complemented
8#10592516C212yesmaximal, complemented
9#10592463C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic, complemented
11#10592378C211yesmaximal, characteristic, complemented
12#79625—34nomaximal
13C2×#3828—21no—
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17Q8×C3⋊Dic3C2212yes—
18C2×#3755C2212yes—
19#64149C2212yes—
20#64139—21no—
21#64102C2212yes—
22#64099—22no—
23#64099C2212yes—
24#64093—22no—
25#64083C2211yescharacteristic
26#64078—21no—
27#64078C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C32×#106C2211yescharacteristic
31C32×#103C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63659C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63642C2212yes—
38#63641C2212yes—
39#63636C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5570—34no—
43#5553—34no—
44C3×C4×SD16D314yescomplemented
45#5163—38no—
46#5027—34no—
47#5007—34no—
48#4871—38no—
49#4817—38no—
50#4764—38no—
51#4694—34no—
52#4679—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#638—22no—
57C2×#638—22no—
58#3828—44no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×#634—21no—
64C2×#634D411yescharacteristic
65C32×SD16—22no—
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2311yescharacteristic
70C32×C4⋊C4C2311yescharacteristic
71C32×C22⋊C4—21no—
72C32×C42—21no—
73C32×C42C2311yescharacteristic
74#3755—24no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)C2312yes—
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3368—91noSylow
87C2×#235—64no—
88C2×C3×SD16C2×D314yes—
89C3×C4×Q8C2×D314yes—
90C3×C4×D4C2×D314yes—
91Q8×Dic3—38no—
92C2×#215—38no—
93#940—38no—
94#930—64no—
95#893—38no—
96#890—38no—
97#890—68no—
98#884—68no—
99#874—34no—
100#869—34no—
101#869—64no—
102C4×Dic6—34no—
103C4×Dic6—64no—
104C3×#106C2×D314yes—
105C3×#103C2×D314yes—
106C3×#102C2×D314yes—
107C3×C4×C8C2×D314yes—
108#832—38no—
109#821—38no—
110#821—38no—
111#815—38no—
112Dic3⋊C8—38no—
113#809—38no—
114#807—38no—
115C4⋊(C3⋊C8)—34no—
116C23×C32—21no—
117C22×C3⋊D3—22no—
118C32×Q8—21no—
119C32×Q8#4112yescomplemented
120C32×D4—21no—
121C32×D4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129#638—44no—
130#638—82no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—42no—
137C4⋊(C3⋊D3)—81no—
138C4×C3⋊D3—44no—
139#634—22no—
140#634—42no—
141C32×C8—21no—
142C32×C8—21no—
143C3⋊(C3⋊C8)—22no—
144#557—91no—
145#550—91no—
146#490—92no—
147#486—91no—
148#478—92no—
149#474—91no—
150#460—92no—
151#460—91no—
152#446—91no—
153#440—92no—
154C4×SD16C3⋊D311yescharacteristic, complemented
155C2×C3×Q8C22×D314yes—
156C2×C3×D4C22×D314yes—
157C22×C3×C4—24no—
158C2×#67—68no—
159C2×#67—68no—
160#235—1216no—
161C2×D12—38no—
162C2×D12—64no—
163C2×D12—64no—
164C2×C4×D3—68no—
165C2×Dic6—34no—
166C2×Dic6—64no—
167C3×SD16—28no—
168C2×C3×C8C22×D314yes—
169C2×C3×C8C22×D314yes—
170C3×C4⋊C4—24no—
171C3×C4⋊C4C22×D314yes—
172C3×C4⋊C4C22×D314yes—
173C3×C22⋊C4—24no—
174C3×C42—24no—
175C3×C42C22×D314yes—
176#215—616no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—34no—
179C4⋊Dic3—38no—
180C4⋊Dic3—68no—
181C4⋊Dic3—68no—
182C4⋊Dic3—64no—
183Dic3⋊C4—38no—
184Dic3⋊C4—68no—
185C4×Dic3—38no—
186C4×Dic3—68no—
187C2×C3⋊C8—38no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C32×C4—22no—
196C32×C4—21no—
197C32×C4—41no—
198C32×C4—41no—
199C32×C4AGL(1,ℤ/8)12yes—
200C32×C4C2×#4111yescharacteristic
201C32×C42−1+411yescharacteristic
202C3⋊Dic3—22no—
203C3⋊Dic3—22no—
204C3⋊Dic3—42no—
205C2×#41—181no—
206C2×SD16—92no—
207C2×SD16C2×C3⋊D311yescharacteristic
208C4⋊Q8—91no—
209C4⋊Q8—181no—
210#127—92no—
211#127—91no—
212#125—92no—
213#125—182no—
214#121—182no—
215#121—181no—
216C4×Q8—91no—
217C4×Q8—92no—
218C4×Q8—181no—
219C4×Q8C2×C3⋊D311yescharacteristic
220C4×D4—92no—
221C4×D4C2×C3⋊D311yescharacteristic
222#107—92no—
223#106C2×C3⋊D311yescharacteristic
224C4⋊C8—92no—
225C4⋊C8—91no—
226#103C2×C3⋊D311yescharacteristic
227#102—92no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102C2×C3⋊D311yescharacteristic
232#97—92no—
233C4×C8C2×C3⋊D311yescharacteristic
234C23×C3—24no—
235C22×D3—68no—
236C3×Q8—24no—
237C3×Q8#23518yescomplemented
238C3×D4—24no—
239C3×D4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—24no—
243C2×C3×C4—48no—
244C2×C3×C4D3×D414yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4C23×D314yes—
247#67—1216no—
248#67—248no—
249C2×Dic3—38no—
250C2×Dic3—38no—
251C2×Dic3—68no—
252D12—68no—
253D12—68no—
254D12—128no—
255D12—244no—
256C4×D3—1216no—
257Dic6—68no—
258Dic6—128no—
259C3×C8—24no—
260C3×C8—24no—
261C3⋊C8—68no—
262C2×C32—81no—
263C2×C32#54811yescharacteristic
264C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
265C2×C32#57711yescharacteristic
266C3⋊D3—82no—
267#41—364no—
268C2×Q8—91no—
269C2×Q8—181no—
270C2×Q8C22×C3⋊D311yescharacteristic
271C2×D4—92no—
272C2×D4—182no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—21no—
278C22×C4—182no—
279SD16—22no—
280SD16—184no—
281C2×C8—92no—
282C2×C8C22×C3⋊D311yescharacteristic
283C2×C8C22×C3⋊D311yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—91no—
286C4⋊C4—92no—
287C4⋊C4—92no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4C22×C3⋊D311yescharacteristic
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—182no—
296C42—21no—
297C42—92no—
298C42—182no—
299C42C22×C3⋊D311yescharacteristic
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3C2×D3×D414yes—
304C2×D3—128no—
305C2×D3—128no—
306C2×D3—128no—
307C3×C4—24no—
308C3×C4—28no—
309C3×C4—44no—
310C3×C4—44no—
311C3×C4#91418yes—
312C3×C4C2×#23514yes—
313C3×C4#101014yes—
314Dic3—68no—
315Dic3—68no—
316Dic3—128no—
317C32#336811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—182no—
320Q8—21no—
321Q8—182no—
322Q8—362no—
323Q8#382812yescomplemented
324D4—21no—
325D4—21no—
326D4—182no—
327D4—182no—
328D4—364no—
329D4—362no—
330D4—721no—
331D4—722no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—182no—
339C2×C4—364no—
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—21no—
344C8—21no—
345C8—182no—
346C2×C3—84no—
347C2×C3#555214yes—
348C2×C3C2×#91414yes—
349C2×C3#577014yes—
350D3—248no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22C2×D4×C3⋊D311yescharacteristic
358C4—21no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—182no—
363C4—182no—
364C4—362no—
365C4#6412312yes—
366C4C2×#382811yescharacteristic
367C4#6436711yescharacteristic
368C3#7962514yescomplemented
369C2—81no—
370C2—722no—
371C2#1059602311yescharacteristic
372C2C2×#6412311yescharacteristic
373C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radical#10596024C2
hypercenterC4×SD16C3⋊D3
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596041C2semidirect
3. C32×C4×SD16C2semidirect
4. #10592862C2semidirect
5. #10592726C2semidirect
6. #10592706C2semidirect
7. #10592570C2semidirect
8. #10592516C2semidirect
9. #10592463C2semidirect
10. #10592393C2semidirect
11. #10592378C2semidirect
44. C3×C4×SD16D3semidirect
119. C32×Q8#41semidirect
154. C4×SD16C3⋊D3semidirect
237. C3×Q8#235semidirect
317. C32#3368semidirect
323. Q8#3828semidirect
368. C3#79625semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105960412
#105960242
C32×C4×SD162
#105928622
#105927262
#105927062
#105925702
#105925162
#105924632
#105923932
#105923782
#796253